This pregnancy for us was not planned and H is still finishing up school (as technically am I but I also have a business) so we are living off my income alone. Because of a bad accident I had in 2009 all of my savings are gone and I actually have debt now so we aren't in the place we wanted to be financially when we planned to start a family. But, we'll deal! Here are some suggestions:
1) Start saving what you can. We can't because we still have debt, but we did sell off some of our frivolous things in order to pay down our debt faster. I also downgraded my car to get lower payments on that. We also became a one-car family and I started carpooling with my car which brings in a lot of extra savings.
2) Look into programs like WIC for some food savings. If you are in school your college may also have programs available for you as well. Mine has a clinic where you can get free ultrasounds and parenting classes.
3) Buy everything used. With the exception of car seats and cribs there aren't many baby related things that you can't buy used. And even cribs and car seats can be used if you know who you are buying from and the history of the item.
4) Look into cloth diapering. It can save you thousands over your child's pre-potty training years. Also breast feeding rather than formula feeding.
5) If you or your SO smoke, quit. If you drink, quit. If you eat out, quit. If you pay for cable, look into Netflix or Hulu Plus instead if you feel you need that entertainment. If your cell phone contract is up look into getting a cheaper plan. Make the sacrifices you need to be able to start saving as good as possible. For the most part, everything we gave up I do not miss. I do occasionally miss eating out and going to movies, but that's a small price to pay for financial stability.
6) Coupons are your friend! My H is a crazy couponer and is one of those people who can figure out how to get a ton of stuff for cheap or even free. Toothbrushes and toothpaste are the easiest things. As well as shampoo, conditioner, and body wash. I don't think we've paid for any of that stuff in about a year! It's nice to be able to take care of some basic necessities and then use what money we do have on important things like insurance and bills.